In a factory, 4% of the components produced are defective.
An automatic scanner examines every component and flags some of them. If a component is defective, the probability that the scanner flags it is 0.98. If a component is not defective, the probability that the scanner flags it is 0.05.
Every flagged component is then inspected by hand, and the hand inspection is always correct.
Find the probability that a randomly chosen component is flagged by the scanner.
Given that a component has been flagged, find the probability that it is not defective. Give your answer to 3 significant figures.
The factory manager says that the scanner is unreliable, because more than half of the components it flags turn out not to be defective. Explain why this is not a fair criticism of the scanner, referring to the proportion of components that are defective.
200 exam-style questions on OCR A Level Maths 2.3 Probability, covering 2.3.1 Mutually exclusive and independent events, 2.3.2 Diagrams to assist probability calculations, 2.3.3 Conditional probability (A-level only), 2.3.4 Conditional probability from first principles (A-level only), and 2.3.5 Modelling with probability. Each one has a worked solution and a mark scheme showing where the marks go.